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"If " I=int (dx)/(root(3)(sin^(11)xcosx)...

`"If " I=int (dx)/(root(3)(sin^(11)xcosx))=-A(tanx)^(-(8)/(3))+B(tanx)^(-(2)/(3))+c," then find the value of " 4A+B " .`

Text Solution

Verified by Experts

The correct Answer is:
-3
`I=int(dx)/(sin^(11//3)x cos^(1//3)x)`
`=int(dx)/(tan^(11//3)x cos^(4)x)`
`=int((1+tan^(2)x)sec^(2)xdx)/(tan^(11//3)x)`
`=int((1+t^(2))dt)/(t^(11//3)) " " ("where " tanx=t)`
`=-(3)/(8)t^(-(8)/(3))-(3)/(2)t^(-(2)/(3))+c, " where " t=tanx`
` :. 4A+B=-3`
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